Cardy-Verlinde formula in FRW Universe with inhomogeneous generalized fluid and dynamical entropy bounds near the future singularity

TL;DR

This paper derives a generalized Cardy-Verlinde entropy formula for inhomogeneous fluids in FRW universes, explores its reduction to standard forms, and investigates the universality and violations of dynamical entropy bounds near various cosmological singularities.

Contribution

It introduces a generalized entropy formula for multicomponent fluids with inhomogeneous equations of state, including viscous and modified gravity effects, and studies entropy bounds near singularities.

Findings

The generalized formula reduces to the standard Cardy-Verlinde formula in special cases.

Dynamical entropy bounds are violated near most types of future singularities.

The entropy bound appears universal for regular, non-singular universes.

Abstract

We derive a Cardy-Verlinde-like formula which relates the entropy of the closed FRW universe to its energy, and Casimir energy, for a multicomponent coupled fluid. The generalized fluid obeys an inhomogeneous equation of state. A viscous dark fluid is included, and we include also modified gravity using its fluid representation. It is demonstrated how such an expression reduces to the standard Cardy-Verlinde formula corresponding to the 2d CFT entropy only in some special cases. The dynamical entropy bound for a closed FRW universe with dark components is obtained. The universality of the dynamical entropy bound near a future singularity (of all four types), as well as near the Big Bang singularity, is investigated. It is demonstrated that except from some special cases of Type II and Type IV singularities the dynamical entropy bound is violated near the singularity even if quantum effects are taken into account. The dynamical entropy bound seems to be universal for the case of a regular universe, including the asymptotic de Sitter one.